Solved: Testing for a disease can be made more efficient by combining samples. If the samples from two people are combined and the mixture tests negative, then both samples are negative. On the other hand, one positive sample will always test positive, no matter how many negative samples it is mixed with. Assuming the probability of a single sample testing positive is 0.15, find the probability of a positive result for two samples combined into one mixture. Is the probability low enough so that further testing of the individual samples is rarely necessary?

A lottery that pays off P300 000 000 is made available for 10 000 000 tickets. Each ticket costs P50. Suppose the variable Z gives the net winnings from playing the lottery. What is the expected gain for joining the lottery with only …

A random sample of n= 21 items is taken, resulting in a sample mean x¯= 17.0 with a sample standard deviation of s= 4.9. Assume x is normally distributed and use this information and α 0.05 test the following hypotheses. H0: μ = 16 …

Bag I contain 3 red and 4 black balls and Bag II contain 4 red and 5 black balls. One ball is transferred from Bag I to Bag II and then a ball is drawn from Bag II. The ball so drawn is found to be red. Find the probability that the t…

The proportion of eligible voters in the next corporation election (in tumkur) who will vote for the incumbent is assumed to be 55%. What is the probability that in a random sample of 500 voters less than 49% say they will vote for th…

A group of students got the following scores in a test:6,9,12,15,18 and 21. Consider samples of size 3thag can be drawn from this population. List all the possible samples and the corresponding mean.

A population consist of the values 2,4,6 and 8 a) List all the possible sample size 2 when drawing with replacement and compute the mean of each sample. b)Construct the sampling distribution of the mean. c) Compute the mean, varian…

Q−5: a) An urn contains 5 red balls and 6 blue balls. A ball is drawn randomly, its colour is noted, and then the ball is replaced in the urn. If thisprocess is repeated four times: i. What is the probability of getting two red ba…

a. List the sample space in the given experiment. How many outcomes are possible? b. Construct a table showing the number of defective computers in each outcome and assign this number to this outcome. What is the value of the rand…

A group of students got the following scores in a test:9,12,15,18,21 and 24. Consider samples of size 3thag can be drawn from this population. List all the possible samples and the corresponding mean. Determine and list all possible s…

Determine the t-value based on the sample size n and a 1)n=25 a= 0.01 Df= T-Value = 2)n=15 a= 0.025 Df= T-Value =

A group of students got the following scores in a test:9,12,15,18,21 and 24. Consider samples of size 3thag can be drawn from this population. List all the possible samples and the corresponding determine and list all possible samples…

indicate whether each of the following statements is true or false. if false indicate why. a) if P(A/B) =0,then A and B are mutually exclusive. b) if P(A/B) =0,then A and B are independent. c) if P(A/B) = P(B/A), then P(A)=P(B). d…

How many four-letter words can be formed using the letters of the word WOMAN?

Is it canbe serve or cannot serve, Explain.P(X) = 3 + X for x = 1, 2, 3, 4 3 – X

P(X) = 1225X for 1, 2, 3, 4

A four-digit number is formed using the digits 1, 2, 3, 5, 8, and 9. What is the probability that the number formed is even?

A pair of dice is rolled thrice. What is the probability of getting doubles in the three rolls?

Determine whether the following can serve as the probability distribution of a random variable X. 1. P(X)= 1/7 for x=1, 2, 3, 4, 5, 6, 7 2.P(X)=x-2/3 for x = 1, 2, 3, 4, 5

If 12% of a population of parts defective, what is the probability of randomly selecting 60 parts and finding that 8 more are defective?

Six women and five men walk into an appliance store at the same time. There are five salesperson available to help them.Find the probability that a salesperson will first help at least 2 women.

Determine the Power set of 𝐴 × 𝐵 if 𝐴 = { 7, 8 } and 𝐵 = { 𝑎, 𝑏 }

Two coins are tossed. Let H be the number of tails that occur. Determine the values of the random variable H.

A coin was flipped four times. Let T be the number of tails that come out. A. Construct the probability distribution of the random variable B.Construct the probability histogram

A large logistic manufacturing company has 100 employees specializing in different machines. From them, 20 are proficient in machine P , 45 in machine Q , 30 in machine R , 1 in machine P and Q , 6 in machine Q and R , 5 in machine R …

1.Find the Domain and Range of the following functions if 𝑓: 𝑅 → 𝑅 i) 𝑓(𝑥) = 12 + 𝑙𝑜𝑔 (1 − 𝑥^2 ) ii) 𝑓(𝑥) = 𝑥^2 +1/𝑥^2 +5 2. Find if the functions are surjective, injective and bijective if 𝑓: 𝑅 → 𝑅 i) 𝑓(𝑥) = 𝑥^5 + 5 ii) 𝑓(𝑥) = 𝑒^4𝑥

What percent of the area under the normal curve is between z=2.25 and z=0.85

Problem 1: School A has a mean population IQ of 100 with a standard deviation of 15. A principal of the said school claims that the students in his school have above average intelligence. A random sample of 30 students IQ scores have …

Laverny tosses an unbiased coin. He receives 100 if a head appears and he pays 40 if a tail appears. Find the variance of his gain.

EXPERIMENT 1. Number of rings before the phone is answered 2. Teacher ask the students to finish the test after an hour 3. Number of complaints per day 4. Height of the tallest building in Lucena City 5. Number of Mobile phone…

Two winners will be drawn from 5 SHS teachers (s) and 7 JHS teachers (J). Let W the random variables representing the JHS teachers. Find the values of the random variable W.

Four coins are tossed. Let M be the variable representing the number of heads that occur. Find the values of the rand om variable M and its corresponding probabilities

The number of patients seen in the emergency room in any hour is a random variable represented by x. Find the probability that in a given hour at least 14 patients will arrive. The probability distribution of x is: *

. From a box containing 4 black balls and 3 green balls, 4 balls are drawn in succession. Let Y be a random variable representing the number of green balls that occur.

In a certain town, 40% of the eligible voters prefer candidate A, 10% prefer candidate B, and the remaining 50% have no preference. You randomly sample 10 eligible voters. What is the probability that 4 will…

The probability distribution of X, the number of imperfections per 10 meters of a synthetic fabric in continuous rolls of uniform width, is given by x 01234 f(x) 0.41 0.37 0.16 0.05 0.01 Construct the cumulative distribution func…

Two independent samples of sizes 8 and 7 contained the following values: Sample I : 19 17 15 21 16 18 16 14 Sample II : 16 14 15 19 15 18 16 Do the estimates of the population variance differ significantly at 5% level?

Assume Y is discrete random variable with probability distribution. { 0.2ky+ 0.1 , for y=0,1,2,3,4 P(Y=y) = { 0 , elsewhere Using R programming, apply the suitable coding to identify answer in (a),(b). (a) probability distr…

The table below shows the weight of 21 students (on the left) and the corresponding number of students with that weight (on the right). Compute the Mean of the data below. Weight No. of Students 34 5 39 8 43 2 45 6

Instruction: Solve the following problem. Find and construct the: Sample space (all outcomes) Possible values Properties 1 and 2 Probability Mass Function Histogram 1. Number of Blue balls Four balls are drawn in succession wit…

A basket contains 5 white ball (w) and 5 black ball (b). What is the possible result if you draw 3 balls in random from the basket.let x be the random variable representing the number of black ball that occur.

Refer to Example 8. How large a sample will we need in order to assert with probability 0.95 that the sample mean will not differ from the true mean by more than 1.5. (replacing σ by s is reasonable here because the estimate is ba…

Question 1 In the Monty Hall Problem described by Karl, the correct approach when confronting to the decision of changing or keeping the door is to... Option: never change the door to increase the probability of winning the pri…

how to find the variance and standard deviation of a discrete random variable

A BASKET CONTAINS 5 WHITE BALL (W) AND 5 BLACK BALL (B). WHAT IS THE POSSIBLE RESULT IF YOU DRAW 3 BALLS IN RANDOM FROM THE BASKET. LET X BE THE RANDOM VARIABLE REPRESENTING THE NUMBER OF BALCK BALL THAT OCCUR.

Construct the probability distribution of a particular experiment by following the instructions given to you. A dog gave birth to a litter of six puppies. Three of them are male while the rest are female.if you are to be given th…

The geometric mean of a group of 15 observations was calculated as 12. It was later found that one observation was wrongly read as 19 instead of the correct value 9. Obtain the correct geometric mean of the data.

n a Math test, the mean score is 45 and the standard deviation is 4. Assuming normality, what is the probability that a score picked at random will lie below 45

One of the city's professional football teams (team 1) plays at home and another (team 2) plays away on the same night. A professional football a 0.641 probability of winning a home game and a 0.462 probability of winning an away game…

Mr. Vijay, a retired government servant, is considering investing his money in two proposals. He wants to choose the one that has higher average net present value and lower standard deviations. The relevant data are given below. Can y…

A survey conducted by U.P research institute on the retrenchment exercise done by the result when a random sample of 10 ministries were selected from a population that is normally distributed, show the following number of workers that…

Using the sample space for rolling two dice, illustrates a probability distribution for random variable X respending the sum of the number that appear

Nigeria population consist of three major ethnic group Yoruba(Y), Hausa (H) and Ibo(I), which make up 30%, 60% and 10% of the population respectively. A sample of 80people includes 21from Yoruba, 57 from Hausa and 2 from Ibo. Is there…

Given the computed mean value, µ = 85 and the standard deviation, σ = 5, convert the following raw scores to its z-scores: a.) x = 92

What is the probability of getting an ace when a card is drawn from a deck of cards?

number of computers sold per day at a local computer store are 0,1,2,3, and 4 with the probabilities 0.1, 0.2, 0.3, 0.2, and 0.2 respectively. Find the variance and standard deviation of the distribution

1.It is claimed that the average weight of babies at birth is 3.4 kg. The average weight of a random sample of 30 newly born babies was determined.It was found out that the average weight was 3.1 kg. Is there a reason to believe that …

Probability mass function consists of the values a random variable can assume and the corresponding probabilities of the values.

What is the chance of getting a sum of prime number when the sum of two dice are rolled?

As studied, the average number of hours spent by senior high school students for their online classes a week is 25 hours with a standard deviation of 4 hours. Assuming that the study is is true and the data is normally distributed.

What is the probability of getting a sum that is multiples of 3 when two dice are thrown?

A group of students got the following scores in a test:9,12,15,18,21 and 24. Consider samples of size 3thag can be drawn from this population. construct a sampling distribution of the resulting sample means

A box contains 58 red marbles, 14 yellow marbles, and 28 blue marbles. All the marbles are of the same size. Three marbles are drawn at random from the box, first one, then a second, and then a third. Determine the probability of gett…

between z= -1.36 and z= 2.55

b. If one car is randomly chosen, find the probability that it is traveling more than 78 mph

Find the mean of the probability distribution of the random variable x, which can take only the values 1, 2, and 3. Given that P(1) = 10/33, P(2) = 1/33, and P(3) = 12/33

A basket contains 8 ripe (R) and 6 unripe (U) bananas. If three bananas are taken from the basket one after the other with replacement. Construct table that shows all the possible outcomes of the random experiment and all the values o…

P(z>-2.14)

Suppose three cell phones are tested at random where D represent the defective cell phone and N represent the non-defective cell phone. Let X represents the number of defective cell phones that occur. , show the values of the random v…

Samples of size 3 are taken from the population 7, 8, 3, 4, 5, 6, 9, 2, 1 with replacement and without replacement. Find (1) The mean and standard deviation of the population. (u The mean of each of the sampling distribution of mea…

find the mean of the probability distribution of the random variable x, which can take only the values 1,2 and 3, given that P(1)= 10/33 P (2) =1/33 and P(3)= 12/33

x=1,3,4,5,10 P(X=x)= 0.30, 0.20, 0.10, 0.15, 0.25 Question: a. What is the range of the variable x? b. What is P(3

Global insurance has found that 20% (1 in 5) of all insurance policies are surrendered (cashed in) before their maturity date. Assume that 10 policies are randomly selected from the policies data base What is the probability that: …

The random variable X represents the number of taxi cabs a doctor meets on his way to the hospital. The probability distribution of X is given in the following distribution table. X P(x) 0 0.01 1 0.15 2 0.20 3 0.25 …

Identify the following as discrete or continuous random variables. (a) Q: Total number of points scored in a football game (b)R: Shelf life of a particular drug (c) S: Height of the ocean’s tide at a given location (d)T: T…

Wood paneling can be ordered in thickness of 1/16,1/8,1/4, or3/8inch. The random variable X is the total thickness of paneling in two orders. List the elements in the sample space.

A key ring contains four office keys that are identical in appearance, but only one will open your office door. Suppose you randomly select one key and try it. If it does not fit, you randomly select one of the three remaining k…

Past experience has shown that, on the average, only one in ten wells drilled hits oil. Let X be the random variable that represents the number of drillings until the first success (oil is struck). Assume that the drillings …

A company has 7 applicants, three women and four men. Suppose that the 7 applicants are equally qualified and that no preference is given for choosing either gender. Let X be the random variable described by the number of wo…

Global insurance has found that 20% (1 in 5) of all insurance policies are surrendered (cashed in) before their maturity date. Assume that 10 policies are randomly selected from the policies data base What is the probability that: …

a) Consider a consulting firm in a particular city where past records show that on average 6 customers arrive daily to seek consulting services. The demand for consulting services in the firm is distributed according to a Poisson dis…

a) A movie producer is bringing out a new movie. In order to map out his advertising campaign, he wants to determine whether the movie will appeal most to a particular age group or whether it will appeal equally to all age groups. Th…

Question Three Three different fertilizers were applied to twenty plots and the yields were recorded as follows. A 21 4 30 25 14 B 8 8 12 5 3 8 5 28 10 10 C …

A regional hardware chain is interested in estimating the proportion of their customers who own their own homes. There is some evidence to suggest that the proportion might be around 0.70. Given this, what sample size is required if…

Use the five step process to determine each of the following areas 1. Between z = 0 and z = 2.67 2. Between z = -0.78 and z = -1.95 3. Between 1.27 and z = -2.1 4. To the right of z = 0.33 5. to the Left z = 1.96

Four coins are tossed. Let Y be the random variable representing the number of tails that occur. Find the values of the random variable Y . Construct a probability distribution.

Two coins are tossed.Let H be the number of tails that occur. determine the values of the random variable H

1. A company manufactures fuses. The percentage of non-defective fuses is 95.4%. A sample of 10 fuse was selected. Calculate the probability of selecting at least 3 defective fuses.

The probability that a patient recovers from a delicate heart operation is 0.9. The next 100 patients having this operation, find the probability that (i) between 84 and 95 (inclusive values) survive? (ii) fewer than 86…

three coins are tossed let h be the random variable when head will occur.find the values of the random variable H

A meeting of envoys was attended by 5 koreans and 3 filipinos. if four envoys were selected at random one after the other, determine the values of the variable K representing the number of koreans.

on a final examination in biology, the mean was 75 and the standard deviation was 12. determine the standard score of a student who received a score of 60 assuming that the scores are normally distributed.

1. A company manufactures soaps. The mean mass of the soaps is 300g with variance 52g. A sample of 100soaps was selected. a) Find the probability of selecting soaps more than masses 320g. b) How many soaps will have mass…

The height of learners (in cm) at a high school can be described by the N(174.50,47.61) distribution. If 1000 learners are randomly selected from the school, how many of them would you expect to have a height of less than 160.0 cm?

A short-term insurance company receives seven motor vehicle claims, on average, per day. Assume that the daily claims rate follows a Poisson process. Calculate all the probabilities using the Poisson formula What is the probability t…

Suppose the time spent by a randomly selected student at a campus computer lab has a gamma distribution with mean 20 minutes and variance 80 minutes.

A population consists of the four numbers 1, 2, and 4. List all the possible samples of size n=2 which can be drawn replacement from the population. Find the following a.) Population means b.) Population Variance c.) Popula…

Below is an incomplete probability distribution for a random variable X. x 1 2 3 4 5 6 f(x) 0.15 0.25 0.33 0.09 (a) If f(4) = P(X = 4) = 2P(X = 5), complete the probability distribution above. (b)Construct a pr…

A deck of 52 playing cards has 4 aces. The probability of getting one ace less than zero

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